Work

Bound states in two spatial dimensions in the noncentral case

Year: 2004

Type: article

Abstract: We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman–Schwinger bound in three dimensions. Specifically, counting the number of bound states in a potential gV for g=1 is replaced by counting the number of gi’s for which zero energy bound states exist, and then the kernel of the integral equation for the zero-energy wave functon is symmetrized. One of the keys of the solution is the replacement of an inhomogeneous integral equation by a homogeneous integral equation.

Source: Journal of Mathematical Physics

DOI: 10.1063/1.1639956

Authors: André Martin, Tai Tsun Wu

Institutions: Laboratoire d’Annecy de Physique des Particules, Laboratoire d'Annecy de Physique Théorique, European Organization for Nuclear Research, Harvard University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: U.S. Department of Energy, CERN

Award: G222768804